Data scarcity is a major limiting factor for applying modern machine learning techniques to clinical tasks. Although sufficient data exists for some well-studied medical tasks, there remains a long tail of clinically relevant tasks with poor data availability. Recently, numerous foundation models have demonstrated high suitability for few-shot learning (FSL) and zero-shot learning (ZSL), potentially making them more accessible to practitioners. However, it remains unclear which foundation model performs best on FSL medical image analysis tasks and what the optimal methods are for learning from limited data. We conducted a comprehensive benchmark study of ZSL and FSL using 16 pretrained foundation models on 19 diverse medical imaging datasets. Our results indicate that BiomedCLIP, a model pretrained exclusively on medical data, performs best on average for very small training set sizes, while very large CLIP models pretrained on LAION-2B perform best with slightly more training samples. However, simply fine-tuning a ResNet-18 pretrained on ImageNet performs similarly with more than five training examples per class. Our findings also highlight the need for further research on foundation models specifically tailored for medical applications and the collection of more datasets to train these models.